The free energies of cavity formation in water with and without hydrogen bonding potential were computed from the results of a set of Monte Carlo simulation calculations on pure liquid TIP4P water model and on the same model but with the electrostatic charges turned off (Lennard-Jones liquid). The free energies of cavity formation in the Lennard-Jones liquids are higher than or approximately equal to those in TIP4P water, depending, respectively, on whether the Lennard-Jones size parameter sigma is set equal to 3.15 A, which is the value of sigma for TIP4P water, or to 2.8 A, which is the commonly assumed value for the oxygen-oxygen distance between two hydrogen-bonded water molecules. This result indicates that changes in the hydrogen-bonded structure of water and/or in the orientational degree of freedom of water are not essential features in the production of the large free energy change upon cavity formation.